# Is 0 A Rational Number

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A rational number is any number that can be written as a ratio such as 1/1, 2/1, 2/3, 3/4, etc. An irrational number is any number that we cannot write as a ratio, such as the number pi ( 3.14...) or the square root of 2. 0 would be a rational number. Since zero can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers for example 0 / 1 ; 0 / 2 ; 0 /10. We also observe that when we divide 0 /1 both 0 & 1 are integers and the denominator i.e. ‘1’ is not equal to 0. Thus zero is a rational number.

Example 1:

Is 1 / 0 irrational?

Solution:

If we divide one by zero, the result is undefined. Therefore 1 /0 is neither rational nor irrational. It is conjointly neither real nor unreal. This can be taken as the explanation why 1 /0 is undefined; it is merely a number.

Example 2:

The numbers { 0, 6, 15, 28, 33, 44, 50, 100, 230 and 288 } belong to which of the following subsets of the real numbers?
1. Natural Numbers
2. Whole Numbers
3. Integers
4. Rational Numbers

#### Solution

Natural numbers do not include 0, so this set of numbers does not belong to subset 1.
Based on the definitions of the subsets of the rational numbers, the numbers belong to subsets of Whole numbers, integers and Rational numbers.